Call-by-push-value is a ”semantic machine code”, providing a set of simple primitives from which both the call-by-value and call-by-name paradigms are built. We present its operational semantics as a stack machine, suggesting a term judgement of stacks. We then see that CBPV, incorporating these stack terms, has a simple categorical semantics based on an adjunction between values and stacks. Th...

We develop a bicategorical setup in which one can speak about adjoint 1-morphisms even the absence of genuine identity 1-morphisms. also investigate part 2-representation theory 2-categories extends to this new setup.

Even though Minimalist grammars are more powerful than TAG on the string level, the classes of tree languages the two define are incomparable. I give a constructive proof that if the standard Move operation in Minimalist grammars is replaced by Reset Lowering, every TAG tree language can be generated. The opposite does not hold, so the strong generative capacity of Minimalist grammars with Rese...

The difference between restrictive and appositive relativization is usually represented in syntax as complementation versus adjunction with respect to the antecedent noun. Instead I propose that an appositive relative clause (ARC) is coordinated with its antecedent. This approach avoids problems that come with the adjunction analysis, and it predicts some interesting facts. First consider the s...

A large part of wide coverage Tree Adjoining Grammars (TAG) is formed by trees that satisfy the restrictions imposed by Tree Insertion Grammars (TIG). This characteristic can be used to reduce the practical complexity of TAG parsing, applying the standard adjunction operation only in those cases in which the simpler cubic-time TIG adjunction cannot be applied. In this paper, we describe a parsi...

We define a coherent adjunction in strict $3$-category and we use string diagrams to show that any can be extended an essentially unique way.